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Question

The tangent to the parabola y2=4x at the point where it intersects the circle x2+y2=5 in the first quadrant, passes through the point :

A
(13,43)
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B
(14,12)
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C
(34,74)
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D
(14,34)
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Solution

The correct option is C (34,74)
y2=4x,x2+y2=5
The point of intersection of the two curves in the first quadrant is (1,2).
Equation of tangent to the parabola y2=4x at (x1,y1)=(1,2) is yy1=4(x+x12)
y=x+1
(34,74) passes through the line y=x+1

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